A relaxation wave solution of the FitzHugh-Nagumo equations

Leonid V. Kalachev

doi:10.1007/BF00171222

A relaxation wave solution of the FitzHugh-Nagumo equations

Leonid V. Kalachev

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Abstract

For the system of FitzHugh-Nagumo equations and certain values of parameters, there exists a relaxation wave solution: a moving spatially periodic structure for which one of the dependent variables has intervals of slow and fast changes within its period. An asymptotic expansion for the solution is constructed (as a power series in the small parameter ε) consisting of regular terms and transition layers. Along with the asymptotic expansion, the velocity of the structure, its period, and the distance between “jumps” of one of the functions are determined.

Original language	English
Pages (from-to)	133-147
Number of pages	15
Journal	Journal of Mathematical Biology
Volume	31
Issue number	2
DOIs	https://doi.org/10.1007/BF00171222
State	Published - Jan 1993

Keywords

Excitable media
Moving periodic structure
Singular perturbations

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10.1007/BF00171222

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abstract = "For the system of FitzHugh-Nagumo equations and certain values of parameters, there exists a relaxation wave solution: a moving spatially periodic structure for which one of the dependent variables has intervals of slow and fast changes within its period. An asymptotic expansion for the solution is constructed (as a power series in the small parameter ε) consisting of regular terms and transition layers. Along with the asymptotic expansion, the velocity of the structure, its period, and the distance between “jumps” of one of the functions are determined.",

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AB - For the system of FitzHugh-Nagumo equations and certain values of parameters, there exists a relaxation wave solution: a moving spatially periodic structure for which one of the dependent variables has intervals of slow and fast changes within its period. An asymptotic expansion for the solution is constructed (as a power series in the small parameter ε) consisting of regular terms and transition layers. Along with the asymptotic expansion, the velocity of the structure, its period, and the distance between “jumps” of one of the functions are determined.

KW - Excitable media

KW - Moving periodic structure

KW - Singular perturbations

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SP - 133

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JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

IS - 2

ER -

A relaxation wave solution of the FitzHugh-Nagumo equations

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Keywords

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